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The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…

Statistical Mechanics · Physics 2009-11-07 Alexei Vazquez

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

Probability · Mathematics 2007-05-23 K. B. Athreya , A. P. Ghosh , S. Sethuraman

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

Probability · Mathematics 2015-03-18 Emmanuel Jacob , Peter Mörters

We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices…

Probability · Mathematics 2020-08-12 John Haslegrave , Jonathan Jordan

For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of…

Statistical Mechanics · Physics 2009-11-11 Wen-Xu Wang , Bu Hu , Tao Zhou , Bing-Hong Wang , Yan-Bo Xie

We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…

Probability · Mathematics 2014-03-19 Yury Malyshkin , Elliot Paquette

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

Applications · Statistics 2025-09-16 Clement Lee

In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional…

Probability · Mathematics 2010-04-14 Sander Dommers , Remco van der Hofstad , Gerard Hooghiemstra

Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…

Physics and Society · Physics 2014-12-25 Weituo Zhang , Chjan Lim

The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…

Social and Information Networks · Computer Science 2015-02-10 Chen Avin , Zvi Lotker , David Peleg

In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…

Physics and Society · Physics 2007-05-23 Chen Chen

Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…

Discrete Mathematics · Computer Science 2018-03-30 Jan Dreier , Philipp Kuinke , Peter Rossmanith

Reciprocity characterizes the information exchange between users in a network, and some empirical studies have revealed that social networks have a high proportion of reciprocal edges. Classical directed preferential attachment (PA) models,…

Physics and Society · Physics 2021-08-10 Tiandong Wang , Sidney I. Resnick

The preferential attachment (PA) model is a popular way of modeling dynamic social networks, such as collaboration networks. Assuming that the PA function takes a parametric form, we propose and study the maximum likelihood estimator of the…

Statistics Theory · Mathematics 2022-08-17 Fengnan Gao , Aad van der Vaart

We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to…

Probability · Mathematics 2012-01-31 Graham Brightwell , Malwina J. Luczak

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…

Probability · Mathematics 2018-08-07 Tiandong Wang , Sidney I. Resnick

Preferential attachment (PA) models of network structure are widely used due to their explanatory power and conceptual simplicity. PA models are able to account for the scale-free degree distributions observed in many real-world large…

Social and Information Networks · Computer Science 2014-05-21 James Atwood , Bruno Ribeiro , Don Towsley

Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…

Methodology · Statistics 2025-10-07 Thomas Boughen , Clement Lee , Vianey Palacios Ramirez

We generalize the scale-free network model of Barab\`asi and Albert [Science 286, 509 (1999)] by proposing a class of stochastic models for scale-free interdependent networks in which interdependent nodes are not randomly connected but…

Physics and Society · Physics 2015-06-11 Boris Podobnik , Davor Horvatic , Mark Dickison , H. Eugene Stanley

We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…

Combinatorics · Mathematics 2010-03-02 Alois Panholzer , Georg Seitz